The present invention relates generally to systems and methods for measuring phase characteristics of electromagnetic wavefronts.
Measuring how a wavefront deviates from perfectly diffraction-limited has many applications. As non-limiting examples, measuring deviations, also referred to as xe2x80x9caberrationsxe2x80x9d, in a wavefront produced by an optical system, such as a telescope, can reveal manufacturing flaws in the system, since many optical systems, to function as best as is possible, must produce perfectly diffraction-limited wavefronts. By adding a component to the system that produces a wavefront that is the conjugate of the measured deviations, the system can be made to produce a more diffraction-limited wavefront and, thus, diffraction-limited performance (i.e., best possible performance).
Another example of an application where knowing the aberrations in a wavefront is useful is in correcting human vision. For instance, as noted in U.S. Pat. No. 5,963,300, by measuring deviations from the perfectly spherical in reflections of laser light from the eye of a patient, aberrations of the eye can be measured and, hence, compensated for. In the ""300 patent, light that is reflected from a patient""s eye is passed through two reticles, and the resulting moirxc3xa9 shadow pattern is presented on a screen. An imaging system images the shadow on the screen onto a camera, with subsequent analysis being undertaken of the imaged shadow. The technique of the ""300 patent is based on geometrical or ray-tracing analysis, which as recognized herein requires theoretical assumptions to perform the geometrical analysis that limit the amplitude of the aberrations that can be measured as well as limit the accuracy with which the aberrations can be measured.
With these drawbacks in mind, the present invention provides the solutions below to one or more of them.
A system for determining aberrations in a coherent electromagnetic wavefront includes a reticle that is positioned in the path of the wavefront, and a detector is also positioned in the path. In accordance with this aspect, the light detector is located at a diffraction pattern self-imaging plane relative to the reticle.
A processor receives the output signal from the light detector and determines aberrations in the beam based thereon. The aberrations in the beam represent aberrations in the wavefront due to the medium through which it passes, or an object from which it reflects, or the source of the wavefront itself.
In a preferred, non-limiting embodiment, the processor executes logic that includes determining a phase gradient of the wavefront phase-front, and determining coefficients of polynomials based on the phase-front gradient which quantify the aberrations. The coefficients represent aberrations. Preferably, the gradient is obtained from a frequency domain transformation of the beam, such that the gradient is the derivatives of phases of the wavefront in directions established by the reticle orientation. In a particularly preferred, non-limiting embodiment, the derivatives are determined in at least two directions, and the coefficients are determined by fitting derivatives of a set of known polynomials to the measured gradient.
In another aspect, a method for determining aberrations in an object includes passing a light beam from the object through a reticle, and then determining derivatives that are associated with the light beam subsequent to the light beam passing through the reticle. Using the derivatives, a measure of aberrations in the object can be output.
In yet another aspect, a computer program product includes a computer readable medium having a program of instructions stored thereon for causing a digital processing apparatus to execute method steps for determining aberrations in an object. The product includes means for receiving a representation of a wavefront propagating into the apparatus, and means for determining wavefront aberrations of the representation. Means are provided for fitting the derivatives to known polynomials or derivatives thereof to obtain coefficients of polynomials. The product includes means for outputting a wavefront characterization based at least in part on the coefficients, with the signal representing aberrations in the object.
In still another aspect, an apparatus for detecting aberrations in an object as manifested in a wavefront includes a reticle positioned in a path of the wavefront and a light detector positioned relative to the reticle to receive the diffracted self-image that is associated with the wavefront. The self-imaging distances are at discrete distances from the reticle that are integral multiples of, where p is the period of the reticle and the xcex is the spectral wavelength of the wavefront. A processor receives signals from the light detector that represent the self-image. The processor derives the wavefront phase gradient associated with the wavefront and uses the coefficients of derivatives of polynomials that define the wavefront to determine the wavefront aberrations.
The details of the present invention, both as to its structure and operation, can best be understood in reference to the accompanying drawings, in which like reference numerals refer to like parts, and in which: